In the context of the “dual carbon” goals, reducing emissions and enhancing energy efficiency have become critical priorities across various sectors. The integration of electric vehicles (EVs) and distributed resources into the power system is essential for achieving these objectives. However, the current prevalence of disordered charging for electric vehicles poses significant challenges, such as increased peak-to-valley load differences in residential areas, which threaten grid stability. Moreover, the growing deployment of distributed resources like photovoltaic (PV) systems and energy storage requires effective local consumption strategies. This paper addresses these issues by proposing a master-slave game-based scheduling optimization framework that incorporates segmental regulation of EV charging power and dynamic pricing mechanisms, including carbon trading. The approach aims to enhance economic and low-carbon benefits while promoting load shifting and peak shaving.
The rapid adoption of electric vehicles in China has highlighted the need for intelligent charging strategies. Traditional disordered charging can lead to grid congestion and inefficiencies, especially when combined with intermittent renewable energy sources. Existing research often overlooks the potential of segmental regulation of charging power, where EVs can adjust their charging rates across multiple levels rather than relying on fixed or interruptible charging. This limitation hinders the optimization of charging prices and the flexible coordination between charging loads and distributed resources. Additionally, while some studies have explored dynamic pricing, the integration of carbon trading mechanisms remains underexplored. Our work fills this gap by developing a multi-agent aggregation framework that includes a microgrid operator, an EV aggregator, and a distributed resource aggregator, all engaged in a master-slave game to determine optimal scheduling strategies.
We first establish a scheduling framework where the microgrid operator acts as the leader, setting dynamic charging prices for EVs and electricity sale prices for the distributed resource aggregator. The EV aggregator and distributed resource aggregator serve as followers, responding to these prices by adjusting their operational strategies. A key innovation is the segmental regulation strategy for EV charging power, which allows EVs to flexibly choose charging power levels and durations within their grid connection periods, ensuring that user charging demands are met while optimizing system performance. This strategy is formulated mathematically to handle constraints such as minimum state of charge (SOC) requirements and maximum charging power. For instance, the charging power for each EV can be selected from a set of discrete values, as shown in the equation: $$P_{k}^{\text{EV}} \in [P_{0}^{\text{EV}}, P_{1}^{\text{EV}}, \ldots, P_{\text{max}}^{\text{EV}}]$$ where $P_{k}^{\text{EV}}$ represents the available charging power levels, and $P_{\text{max}}^{\text{EV}}$ is the maximum power. The charging delay coefficient is defined as: $$D_{i}^{l} = \eta (t_{i} – t_{i}^{l} – t_{i}^{\text{con}}) P_{k}^{\text{EV}} – (S_{i}^{\text{min}} – S_{i}^{\text{con}}) C^{\text{EV}}$$ where $\eta$ is the charging efficiency, $t_{i}$ is the grid connection duration, $t_{i}^{l}$ is the delayed charging time, $S_{i}^{\text{min}}$ and $S_{i}^{\text{con}}$ are the minimum and initial SOC, and $C^{\text{EV}}$ is the battery capacity.
The dynamic charging price for EVs is constrained by the average price and power balance equations: $$\pi_{\text{ave}} = \frac{1}{T} \sum_{t=1}^{T} \pi_{t}^{\text{EV}}$$ and $$\sum_{i=1}^{n} P_{i,t}^{\text{EV}} = P_{t}^{\text{EV}} = P_{t}^{\text{DA}} + P_{t}^{\text{MG}}$$ where $\pi_{t}^{\text{EV}}$ is the dynamic charging price, $P_{t}^{\text{DA}}$ is the power purchased from the distributed resource aggregator, and $P_{t}^{\text{MG}}$ is the power from the microgrid operator. The EV aggregator’s objective is to minimize total charging costs, including electricity and carbon trading costs: $$J_{\text{EV}} = \sum_{t=1}^{T} \left( \pi_{t}^{\text{EV}} P_{t}^{\text{EV}} – C_{t}^{\text{EV}} \right)$$ where $C_{t}^{\text{EV}}$ represents carbon trading benefits, calculated based on the reduction in碳排放 compared to conventional vehicles. The carbon emissions from EV charging are modeled as: $$E_{t}^{\text{EV}} = \beta_{t} P_{t}^{\text{EV}} \Delta t q_{\text{EV}}$$ where $\beta_{t}$ is the fossil energy proportion, and $q_{\text{EV}}$ is the carbon emission factor.
The distributed resource aggregator manages PV and energy storage systems, with the goal of minimizing operational costs: $$J_{\text{DA}} = \sum_{t=1}^{T} \left( \pi_{t}^{\text{DA}} P_{t}^{\text{DA}} – C_{t}^{\text{E}} – C_{t}^{\text{PV}} \right)$$ where $C_{t}^{\text{E}}$ and $C_{t}^{\text{PV}}$ are the costs and benefits associated with energy storage and PV generation, respectively. Constraints include charging and discharging limits for storage: $$0 \leq P_{t}^{\text{ESS,c}} \leq u P_{\text{max}}^{\text{ESS}}$$ and $$- (1 – u) P_{\text{max}}^{\text{ESS}} \leq P_{t}^{\text{ESS,d}} \leq 0$$ where $u$ is a binary variable indicating charging or discharging mode. The microgrid operator’s objective combines economic and load variance minimization: $$J_{\text{MG}} = \omega_{1} J_{1} + \omega_{2} J_{2}$$ where $J_{1}$ is the operating cost, and $J_{2}$ is the load variance, with weights $\omega_{1}$ and $\omega_{2}$ summing to 1. The power balance constraint ensures that supply meets demand: $$P_{t}^{\text{EV}} + P_{t}^{\text{L}} = P_{t}^{\text{MT}} + P_{t}^{\text{C}} + P_{t}^{\text{PV}} + P_{t}^{\text{ESS}}$$ where $P_{t}^{\text{L}}$ is the residential load, $P_{t}^{\text{MT}}$ is the gas turbine output, and $P_{t}^{\text{C}}$ is the power purchased from the grid.
To solve the master-slave game, we employ an improved Kriging meta-model that reduces computational complexity and enhances convergence. The game is formulated as: $$\min_{\pi_{t}^{\text{EV}}, \pi_{t}^{\text{DA}}} J_{\text{MG}} \left( P_{t}^{\text{EV}}, P_{t}^{\text{DA}}, P_{t}^{\text{PV}}, P_{t}^{\text{ESS}} \right)$$ subject to the followers’ optimal responses: $$\min_{P_{t}^{\text{EV}}} J_{\text{EV}} \left( \pi_{t}^{\text{EV}} \right)$$ and $$\min_{P_{t}^{\text{PV}}, P_{t}^{\text{ESS}}} J_{\text{DA}} \left( \pi_{t}^{\text{DA}} \right)$$ The Kriging approach efficiently handles the increased variables from segmental regulation, with initial sampling using Latin Hypercube Sampling (LHS) and refinement via particle swarm optimization.
We conducted simulations with 2,000 electric vehicles in a typical microgrid scenario. The EVs have battery capacities of 35 kWh, charging efficiencies of 0.95, and SOC requirements following uniform distributions. The charging power can be adjusted between 1 kW and 7 kW. Time-of-use electricity prices and carbon trading parameters are based on real-world data from China. Four scenarios are compared: Scenario 1 with disordered charging; Scenario 2 with segmented charging under fixed peak-valley prices; Scenario 3 with dynamic pricing and interruptible charging; and Scenario 4 with both dynamic pricing and segmental regulation. The results demonstrate that Scenario 4 achieves the lowest charging costs and operational expenses, while significantly reducing the peak-to-valley load difference by 11.6% compared to disordered charging. The segmental regulation strategy allows EVs to choose optimal charging power and durations, leading to better utilization of PV output and lower carbon emissions. For example, the EV aggregator’s costs decrease by 15.1%, and carbon emissions are reduced due to increased renewable energy consumption.
| Scenario | EV Aggregator Cost ($) | Carbon Emissions (kg) | Peak-to-Valley Difference Rate (%) |
|---|---|---|---|
| 1 (Disordered) | 21,899 | High | 48.5 |
| 2 (Segmented, Fixed Price) | 21,280 | Medium | 39.8 |
| 3 (Dynamic, Interruptible) | 19,130 | Low | 40.9 |
| 4 (Dynamic, Segmented) | 18,589 | Lowest | 36.9 |
The economic benefits are further illustrated by the dynamic charging prices, which fluctuate based on system conditions. For instance, during periods of high PV output, prices are lowered to encourage charging, while during peak load times, prices are adjusted to prevent congestion. The distributed resource aggregator’s sale prices are optimized between upper and lower bounds to incentivize local consumption. The carbon trading mechanism adds a low-carbon dimension, with EVs earning credits for reduced emissions compared to gasoline vehicles. The carbon trading cost for the microgrid operator is calculated as: $$C_{t}^{\text{MT}} = k Q_{t}^{\text{MT}}$$ where $Q_{t}^{\text{MT}}$ is the carbon quota for gas turbines, and $k$ is the carbon price.
In terms of load management, the total load curves show that Scenario 4 avoids the formation of new peaks by dispersing EV charging across off-peak periods. The segmental regulation strategy enables a more flexible response to price signals, with EVs charging at higher power levels for shorter durations when prices are low. This is evident from the probability distribution of charging choices, where over 81% of EVs select charging powers above 5 kW, with 19.25% opting for 7 kW for 3 hours. The SOC profiles confirm that most EVs meet their minimum requirements without exacerbating grid stress. The improved Kriging meta-model proves efficient, converging in 66 iterations on average compared to 267 for genetic algorithms, while yielding lower costs for the microgrid operator.
In conclusion, our proposed method enhances the flexibility of electric vehicle integration through segmental charging power regulation and dynamic pricing within a master-slave game framework. By incorporating carbon trading, it achieves significant economic and low-carbon benefits, reducing operational costs and emissions while improving load leveling. The approach is particularly relevant for China’s evolving EV market, where smart charging strategies can support grid stability and renewable energy integration. Future work could explore real-time implementation and scalability to larger systems.